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wolverine [178]
3 years ago
7

Historical data for a local manufacturing company show that the average number of defects per product produced is 2. In addition

, the number of defects per unit is distributed according to a Poisson distribution. What is the probability that there will be a total of 7 defects on four units
Mathematics
1 answer:
charle [14.2K]3 years ago
8 0

Answer:

The probability that there will be a total of 7 defects on four units  is 0.14.

Step-by-step explanation:

A Poisson distribution describes the probability distribution of number of success in a specified time interval.

The probability distribution function for a Poisson distribution is:

P(X = x)=\frac{e^{-\lambda}\lambda^{x}}{x!}, x=0,1,2,3,...

Let <em>X</em> = number of defects in a unit produced.

It is provided that there are, on average, 2 defects per unit produced.

Then in 4 units the number of defects is, (2\times4)=8.

Compute the probability of exactly 7 defects in 4 units as follows:

P(X = x)=\frac{e^{-\lambda}\lambda^{x}}{x!}\\P(X=7)=\frac{e^{-8}8^{7}}{7!}\\=\frac{0.0003355\times2097152}{5040}\\ =0.1396\\\approx0.14

Thus, the probability of exactly 7 defects in 4 units is 0.14.

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                   ---------------------------------------(1)

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